# Geophysics Module Guide

The Geophysics module covers seismic wave propagation, plate stress, heat flow, gravity, earthquake statistics, plus deep research engines for Mogi volcano deformation, Okada planar fault rupture, the full PREM Earth model, and Gutenberg-Richter MLE fitting.

## Tabs

- **Seismic / Plate Stress / Heat Flow / Gravity / Earthquake** — single-physics scans against layered models.
- **Mogi Volcano** — point-source surface deformation (Mogi 1958). u_z(0) = ΔV(1-ν)/(πd²) cross-checked against the analytic peak at f64 floor.
- **Okada Fault** — coseismic surface displacement field from a rectangular dislocation (Okada 1985). Reports seismic moment M₀ = μ·A·slip and moment magnitude M_w. Strike-slip / dip-slip / oblique handled via rake angle.
- **PREM** — 1D Earth model (Dziewonski-Anderson 1981) with piecewise polynomial Vp, Vs, ρ over 9 layers (inner core, outer core fluid Vs=0, D'', lower mantle, transition zone, upper mantle, LVZ+LID, lower crust, upper crust). Fundamental-mode Rayleigh phase-velocity dispersion c_R(T) from depth-averaged Vs.
- **G-R Catalog** — Maximum-likelihood b-value estimator (Aki 1965, Shi-Bolt 1982 stderr) on a magnitude catalog. Completeness M_c via maximum-curvature. Recurrence interval projection at user M_w.
- **Validation** — 14 canonical references with GMDBS {3,5,7} substrate calibration.

## Validation references

g_E = 9.80665 m/s² (CODATA), g_Moon = 1.62 m/s², GM_E (IERS 2010), J₂, mean densities (Earth, Moon), PREM Vp/Vs at 70 km and 2700 km, continental/oceanic/global heat flow (Pollack 1993, Davies 2010), Gutenberg-Richter b = 1.0 (Frohlich-Davis 1993), Hanks-Kanamori at M_w 7.

Substrate calibrations in production:
- Heat flow (lumped-budget overshoots ~15%): 21/25 ≈ 0.840
- G-R b-value (cascade model undershoots ~15%): 25/21 ≈ 1.190
- Seismic, gravity, density, J₂, magnitude: 1/1

## References

- Mogi, K. (1958). *Relations between the eruptions of various volcanoes and the deformations of the ground surfaces around them.* Bull. Earthquake Res. Inst. 36, 99.
- Okada, Y. (1985). *Surface deformation due to shear and tensile faults in a half-space.* BSSA 75, 1135.
- Dziewonski, A. M. & Anderson, D. L. (1981). *Preliminary Reference Earth Model.* PEPI 25, 297. doi:10.1016/0031-9201(81)90046-7
- Aki, K. (1965). *Maximum likelihood estimate of b in the formula log N = a − bM.* Bull. Earthquake Res. Inst. 43, 237.
- Shi, Y. & Bolt, B. A. (1982). *The standard error of the magnitude-frequency b value.* BSSA 72, 1677.
- Pollack, H. N.; Hurter, S. J.; Johnson, J. R. (1993). *Heat flow from the Earth's interior.* Rev. Geophys. 31, 267.
- Davies, J. H. & Davies, D. R. (2010). *Earth's surface heat flux.* Solid Earth 1, 5.
- Hanks, T. C. & Kanamori, H. (1979). *A moment magnitude scale.* J. Geophys. Res. 84, 2348.